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Mixed Finite Volume Element Method for Vibration Equations of Beam with Structural Damping
College of Mathematics and Statistics, Shandong Normal University, Jinan, China
College of Mathematics and Statistics, Shandong Normal University, Jinan, China
College of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 1 College of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 2 College of Mathematics and Statistics, Shandong Normal University, Jinan, China
- 3 College of Mathematics and Statistics, Shandong Normal University, Jinan, China
American Journal of Computational Mathematics·Volume 11 (2021)·Pages 207–225·Published 27 September 2021·DOI10.4236/ajcm.2021.113014
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Abstract
In this paper, for the initial and boundary value problem of beams with structural damping, by introducing intermediate variables, the original fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed . Numerical examples are provided to confirm the theoretical results. In the end, we test the value of δ to observe its influence on the model.
KeywordsVibration EquationsStructural DampingMixed Finite Volume Element MethodError EstimationNumerical Simulation
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